WASHINGTON — House Republicans appeared Wednesday to be rallying around an $85 billion deal to avert another government shutdown, brushing off complaints from their right wing that the effort would trade immediate spending cuts for less-certain long-term savings.

After conducting a series of closed-door briefings and polling members during a late-afternoon vote, GOP leadership aides confidently predicted that the deal struck between House Budget Committee Chairman Paul Ryan, R-Wis., and Senate Budget Committee Chairwoman Patty Murray, D-Wash., would sail through the House when it comes to a vote Thursday.

The moment seemed to mark a potentially significant shift by House Republicans away from the uncompromising confrontation of recent years and toward a determined era of more functional governance. After multiple standoffs and threatened defaults and a government shutdown, polls show the Republican brand has been damaged among voters, and even some of the most conservative Republicans said they were ready for a breather.

“That’s the only reason” to vote for the budget deal. “To calm things down,” said Rep. Cynthia Lummis, R-Wyo., who said she was undecided about the measure. “To reset the debate is a great way to describe it.”

The only sign of trouble came from archconservatives who routinely buck House Speaker John Boehner, R-Ohio. But they acknowledged that their government-shrinking priorities had been abandoned in favor of Republican concerns about the Pentagon budget and political fallout from another shutdown.

Independent conservative groups with a proven ability to sway Republicans continued to batter the agreement, which would cancel half of the sharp automatic budget cuts in the current fiscal year and replace them with a mix of fees and other savings. On Wednesday, Chris Chocola, president of the conservative Club for Growth, complained that the plan “swaps debt reduction today and next year for the dubious promise of debt reduction a decade from now.”

But Boehner fired back during a brief news conference Wednesday, suggesting that the Club for Growth, Heritage Action for America and other groups were vilifying a reasonable proposal to fuel their own fundraising campaigns.

“They’re using our members and they’re using the American people for their own goals,” Boehner said. “This is ridiculous.”

Glen Bolger, a leading Republican pollster, said the budget deal gives House Republicans a choice: They can pass a compromise that represents progress toward the goal of reducing the size of government, or they can reject the deal as insufficiently conservative and cement the party’s reputation for obstruction.

“We are either a party that is serious about governing when control of Washington is split, or we are an unserious party that doesn’t care about realistic incremental gains, only about unrealistically getting the whole ball of wax, which will never happen as long as there is a Democratic president and a Democratic [Senate] majority leader,” Bolger said.

The ‘doc fix’

Though they anticipate a strong Republican vote, GOP leadership aides said they were likely to need a sizable contingent of Democrats to push the measure across the finish line. Given President Barack Obama’s strong support for the budget deal, Democrats, too, were expected to vote for the measure in large numbers.

That margin may be trimmed somewhat, key Democrats said, by a last-minute decision by Republicans to add an amendment to benefit doctors who see Medicare patients.

Democrats support the “doc fix,” which would postpone for three months a 24 percent cut in Medicare reimbursement rates set to hit providers in January. But they protested a decision Wednesday by GOP leaders to help doctors while refusing to extend unemployment insurance for the long-term unemployed, which is set to expire at the end of the month, cutting off 1.3 million people.

“It’s unconscionable,” said Rep. Sander Levin of Michigan, the senior Democrat on the House Ways and Means Committee. “Are we going to leave here saying we’ll reimburse physicians and cut off people who have been left out of a job through no fault of their own?”

Rep. Chris Van Hollen of Maryland, the lead budget negotiator for House Democrats, said the wrinkle adds “a new dynamic that could upset the apple cart” for the painstakingly crafted budget deal.

Other Democrats said the deal was in no real danger.

And in a speech on the Senate floor, Senate Majority Leader Harry Reid of Nevada dismissed the effort by House Democrats to extend unemployment benefits before the Christmas break, saying he would “push here after the first of the year for an extension of emergency unemployment insurance.”

Reid said he was disappointed that jobless benefits were not included in the budget deal. But he added: “Neither side got everything it wanted in these negotiations.”

Deficit targets

In an official estimate released Wednesday, the nonpartisan Congressional Budget Office said the budget measure would reduce deficits by $85 billion over the next decade by reducing taxpayer contributions to federal-worker pensions, requiring private companies to pay higher premiums for federal insurance of their pensions, and increasing security fees for airline travelers, among other changes.

Of that $85 billion, the CBO said $62 billion would go toward rolling back the automatic budget cuts in fiscal 2014 and 2015, with the Pentagon and domestic programs benefiting equally. The rest of the savings, roughly $23 billion, would go toward trimming deficits projected to exceed $6 trillion over the next decade.

If the House approves the package as expected, the Senate plans to take it up next week before leaving town for Christmas. Members of the House and Senate Appropriations committees would then work over the holidays to prepare funding bills for individual agencies, which are likely to be combined into a single measure.

While the agreement between Ryan and Murray lessens the odds of another shutdown when a temporary spending bill expires Jan. 15, the overall funding measure must pass before that deadline to keep the government open.

That would give Congress relatively clear sailing on the budget until the fall of 2015 — except for the need to raise the federal debt limit, probably sometime in late February or early March.

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